NDLI: Ambiguity and Deficiency of Permutations Over Finite Fields With Linearized Difference Map

Content Provider	IEEE Xplore Digital Library
Author	Panario, D. Sakzad, A. Stevens, B. Thomson, D. Qiang Wang
Copyright Year	1963
Abstract	The concepts of ambiguity and deficiency for a bijection on a finite Abelian group were recently introduced. In this paper, we present some further fundamental results on the ambiguity and deficiency of functions; in particular, we note that they are invariant under the well-known Carlet-Charpin-Zinoviev-equivalence, we obtain upper and lower bounds on the ambiguity and deficiency of differentially k-uniform functions, and we give a lower bound on the nonlinearity of functions that achieve the lower bound of ambiguity and deficiency. In addition, we provide an explicit formula in terms of the ranks of matrices on the ambiguity and deficiency of a Dembowski-Ostrom (DO) polynomial, and using this technique, we find exact values for known cases of DO permutations with few terms. We also derive exact values for the ambiguities and deficiencies of DO permutations obtained from trace functions. The key relationship between the above polynomials is that they all have linearized difference map.
Sponsorship	IEEE Information Theory Society
Starting Page	5616
Ending Page	5626
Page Count	11
File Size	2802452
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Cryptography Galois fields Upper bound Additives Educational institutions Atmospheric measurements permutation polynomials Ambiguity deficiency Dembowski–Ostrom (DO) polynomials finite fields linearized polynomials nonlinearity
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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